In the course of arbitration proceedings facts apparently criminal may arise that, being materially relevant for deciding the arbitration, should be tried by a competent criminal court forming a criminal preliminary issue in the arbitration proceedings. Law on Arbitration (LA) does not contain any provision regulating this kind of matters and the opportunity to do it through the reform of the said LA as carried out by Act 11/2011, of 20th May, has been missed. Consequently, new solutions should be proposed to solve a case of this kind as there concur in arbitration proceedings the same grounds as in civil proceedings for the existence of criminal preliminary issues. The main solution emerges from conceiving the occurrence of a criminal preliminary issue in arbitration proceedings, and also in civil proceedings, as having an absolute restrictive character. Therefore, it is extremely exceptional evidencing the necessary conditions for the existence of a criminal preliminary issue; secondly, in the event all the required circumstances were met, we would resort to the analogical application of those provisions regulating criminal preliminary issues in civil proceedings (arts. 40 ss LEC and art. 10.2 LOPJ) what would bring forward the stay of the arbitration proceedings and the subsequent binding effect of the decision adopted within the criminal action; additionally, among others, the controversy may be decided upon but bearing in mind the purportedly criminal underlying facts though without necessarily supplying them that character. All of them present advantages and disadvantages that season the analysis of this investigation concluding with the study of criminal preliminary issues at the stage of the enforcement of the arbitration award where art. 569 LEC would be applicable that establishes the suspension of the enforcement of the award when the criminal facts determine the falsehood or the nullity of the enforceable title or the invalidity or unlawfulness of the decision of enforcement.